{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:E4VVQZ4IDCL5YZ33QP4HPPL2IE","short_pith_number":"pith:E4VVQZ4I","canonical_record":{"source":{"id":"2605.15973","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-15T14:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"88ce40ccd4b9897a6d4b2abcb0a0956b921a596268fb06f070019f651d24aada","abstract_canon_sha256":"92128980182096786399499dbd4ecbeb2cf29ba5402905a06c1c49f22f3dd460"},"schema_version":"1.0"},"canonical_sha256":"272b5867881897dc677b83f877bd7a413b8392445d2f810cfea87ff0b1517a4b","source":{"kind":"arxiv","id":"2605.15973","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15973","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15973v1","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15973","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"E4VVQZ4IDCL5","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"pith_short_16","alias_value":"E4VVQZ4IDCL5YZ33","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"pith_short_8","alias_value":"E4VVQZ4I","created_at":"2026-05-20T00:01:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:E4VVQZ4IDCL5YZ33QP4HPPL2IE","target":"record","payload":{"canonical_record":{"source":{"id":"2605.15973","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-15T14:04:58Z","cross_cats_sorted":[],"title_canon_sha256":"88ce40ccd4b9897a6d4b2abcb0a0956b921a596268fb06f070019f651d24aada","abstract_canon_sha256":"92128980182096786399499dbd4ecbeb2cf29ba5402905a06c1c49f22f3dd460"},"schema_version":"1.0"},"canonical_sha256":"272b5867881897dc677b83f877bd7a413b8392445d2f810cfea87ff0b1517a4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:01:47.250094Z","signature_b64":"Sf6llhlhNcKpa9poXgsmWFSX+gxqLjcRom8kDA1bTko3JO2B82JFeb/IcA3YUhFqIgz9ptdb9hAyExpQo3/4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"272b5867881897dc677b83f877bd7a413b8392445d2f810cfea87ff0b1517a4b","last_reissued_at":"2026-05-20T00:01:47.249363Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:01:47.249363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.15973","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:01:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RAYGOMcwgtOv7/JHc2PnMocM3bVXdL2Xu2gvGR8fnpUdfUqn6iydbeey+zJEqE3C7QA2izW64sxIZ2K892ynBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:55:55.333655Z"},"content_sha256":"675d5f84aa19ce92e6f7c2b71f622141a776a9c4098ce65cae3c97b94de02872","schema_version":"1.0","event_id":"sha256:675d5f84aa19ce92e6f7c2b71f622141a776a9c4098ce65cae3c97b94de02872"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:E4VVQZ4IDCL5YZ33QP4HPPL2IE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rate of convergence to steady state in a linear chromatography model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Joaqu\\'in Menacho, J. Sol\\`a-Morales, Marta Pellicer","submitted_at":"2026-05-15T14:04:58Z","abstract_excerpt":"We study the rate of convergence to the steady state in the True Moving Bed model of linear chromatography, as a function of the six parameters that appear in the model. The model is a system of eight linear partial differential equations of hyperbolic type, coupled through the equations themselves and also through boundary conditions. We prove that the rate of convergence is given by a dominant eigenvalue, whose existence we prove by means of the Krein-Rutman Theorem, and by comparison arguments. We show how to construct a (not at all simple) characteristic function, whose roots are the eigen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15973","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15973/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:44.866766Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.686890Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"fe94aa475cb65668da973b01bbc2b1c0065e8099b56d67f22f1bc2d1997a448f"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:01:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LhHgGNZMwlJuz0xxVXzF+0N6lOr6UXKdGJBhINRiO5ngq25ud5KVFwM5+LVDRTaGh26MhCjDolL/Tu44+3FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T06:55:55.334482Z"},"content_sha256":"6b0c43eafccc27dd89128e409d5a20ac6acbbeb395c0fea665dac6c98eb7ca81","schema_version":"1.0","event_id":"sha256:6b0c43eafccc27dd89128e409d5a20ac6acbbeb395c0fea665dac6c98eb7ca81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E4VVQZ4IDCL5YZ33QP4HPPL2IE/bundle.json","state_url":"https://pith.science/pith/E4VVQZ4IDCL5YZ33QP4HPPL2IE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E4VVQZ4IDCL5YZ33QP4HPPL2IE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T06:55:55Z","links":{"resolver":"https://pith.science/pith/E4VVQZ4IDCL5YZ33QP4HPPL2IE","bundle":"https://pith.science/pith/E4VVQZ4IDCL5YZ33QP4HPPL2IE/bundle.json","state":"https://pith.science/pith/E4VVQZ4IDCL5YZ33QP4HPPL2IE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E4VVQZ4IDCL5YZ33QP4HPPL2IE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:E4VVQZ4IDCL5YZ33QP4HPPL2IE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"92128980182096786399499dbd4ecbeb2cf29ba5402905a06c1c49f22f3dd460","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-15T14:04:58Z","title_canon_sha256":"88ce40ccd4b9897a6d4b2abcb0a0956b921a596268fb06f070019f651d24aada"},"schema_version":"1.0","source":{"id":"2605.15973","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15973","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15973v1","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15973","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"pith_short_12","alias_value":"E4VVQZ4IDCL5","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"pith_short_16","alias_value":"E4VVQZ4IDCL5YZ33","created_at":"2026-05-20T00:01:47Z"},{"alias_kind":"pith_short_8","alias_value":"E4VVQZ4I","created_at":"2026-05-20T00:01:47Z"}],"graph_snapshots":[{"event_id":"sha256:6b0c43eafccc27dd89128e409d5a20ac6acbbeb395c0fea665dac6c98eb7ca81","target":"graph","created_at":"2026-05-20T00:01:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:44.866766Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.686890Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.15973/integrity.json","findings":[],"snapshot_sha256":"fe94aa475cb65668da973b01bbc2b1c0065e8099b56d67f22f1bc2d1997a448f","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the rate of convergence to the steady state in the True Moving Bed model of linear chromatography, as a function of the six parameters that appear in the model. The model is a system of eight linear partial differential equations of hyperbolic type, coupled through the equations themselves and also through boundary conditions. We prove that the rate of convergence is given by a dominant eigenvalue, whose existence we prove by means of the Krein-Rutman Theorem, and by comparison arguments. We show how to construct a (not at all simple) characteristic function, whose roots are the eigen","authors_text":"Joaqu\\'in Menacho, J. Sol\\`a-Morales, Marta Pellicer","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-15T14:04:58Z","title":"On the rate of convergence to steady state in a linear chromatography model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.15973","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:675d5f84aa19ce92e6f7c2b71f622141a776a9c4098ce65cae3c97b94de02872","target":"record","created_at":"2026-05-20T00:01:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"92128980182096786399499dbd4ecbeb2cf29ba5402905a06c1c49f22f3dd460","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2026-05-15T14:04:58Z","title_canon_sha256":"88ce40ccd4b9897a6d4b2abcb0a0956b921a596268fb06f070019f651d24aada"},"schema_version":"1.0","source":{"id":"2605.15973","kind":"arxiv","version":1}},"canonical_sha256":"272b5867881897dc677b83f877bd7a413b8392445d2f810cfea87ff0b1517a4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"272b5867881897dc677b83f877bd7a413b8392445d2f810cfea87ff0b1517a4b","first_computed_at":"2026-05-20T00:01:47.249363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:47.249363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sf6llhlhNcKpa9poXgsmWFSX+gxqLjcRom8kDA1bTko3JO2B82JFeb/IcA3YUhFqIgz9ptdb9hAyExpQo3/4DQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:47.250094Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15973","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:675d5f84aa19ce92e6f7c2b71f622141a776a9c4098ce65cae3c97b94de02872","sha256:6b0c43eafccc27dd89128e409d5a20ac6acbbeb395c0fea665dac6c98eb7ca81"],"state_sha256":"10b2cd1a8702650e3676e49f593d66dea8762fe18d288db0794db9b80e4b7f76"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/UjlkkYEtaqDdJBt17eHTbn3p5DRwTMJKYTBCMy7a0zCOyHvNF1WY+JVKXwrdcYxU4IFbAmgJlhY9K5Qi4/DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T06:55:55.338908Z","bundle_sha256":"bc89f5cd6a1bd1e8ecbfb7cab4bb5d3540d9b7856b713c388da8f17cdd61fe49"}}